I had a few problems in theh past with my drivers door sensor doing the same thing.
I think its an electrical connection that completes the circuit when you shut the door to shut off the stupid chime. take some rag or sandpaper depending on what kind of erossion is between the latch on the door and the door post and make sure its clean. This way it gets a good connection. thats how i got miine to work.
if your alarm is going off, it may also be a short in the wiring in the door. often times from the door opening and closing all the time the wires that go from the door to the car get brittle and will break.
One final thing you could try is unplug the connection for the drivers door, when doing this it will be as if the door is closed all the time and your inside lights wont come on when opening the door. kind of a pain, but it wont chime all the time while your driving. this is what I actually have for my front passenger door, all the other doors are working. to unplug this its located by the front passenger side kick pannel. pull the carpet up and you will see a bunch connections. you will just have to try unplugging each one until you see that its the one for the drivers door.
Hope that helps.
Scott
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